Endrenyi L, Hao Y
Department of Pharmacology, University of Toronto, Ontario, Canada.
Int J Clin Pharmacol Ther. 1998 Aug;36(8):450-7.
Tradeoff between changes of intraindividual variations of 2 drug formulations and of the difference between their means is a characteristic of a procedure suggested for the determination of individual bioequivalence [Schall and Luus 1993] and to be proposed by the Food and Drug Administration for adoption. Hauck et al. [1996] investigated properties of the tradeoff. Their procedure was applied and extended in the present study. The tradeoff was shown to be asymmetric. Notably, a small change in intrasubject variations can elicit, under various conditions, a comparatively large change in the allowable difference between means which can still be compatible with the declaration of bioequivalence. For instance, when the intraindividual coefficients of variations are 40% and 38% for the reference and test formulations, respectively, the allowable difference between means may increase, as a benefit, by 12.3%. A penalty by 11.2% is elicited if the intrasubject variations of the reference and test products are 40 and 42%, respectively. In addition, 4-period crossover trials were simulated. Ratios of estimated variances of the 2 formulations followed an F-distribution. Distributions of changes in allowable deviations between means were calculated from the tradeoff relationships; generally substantial changes were noted with high probabilities. For example, with an intraindividual variation of 30% there is an estimated 37% probability that a benefit of 10% increase, or larger, is gained by chance in the allowable difference between means, and an additional 36% probability that a penalty of a 10%, or larger, decrease in the allowable difference is suffered. With an intrasubject variation of 40%, the estimated probabilities are 42% and an additional 42% for a 10% expansion and contraction, respectively, of the allowable difference between means. Consequently, the strong asymmetry of the tradeoff could result in very large probabilities for benefits and penalties. Therefore, the investigated model assessing individual bioequivalence does not appear to be suitable for implementation.
两种药物制剂个体内变异的变化与它们均值差异之间的权衡是一种用于确定个体生物等效性的方法的特征[Schall和Luus，1993年]，并且将由美国食品药品监督管理局提议采用。Hauck等人[1996年]研究了这种权衡的性质。他们的方法在本研究中得到应用和扩展。结果表明这种权衡是不对称的。值得注意的是，在各种条件下，个体内变异的微小变化可能会引发均值之间允许差异的相对较大变化，而这种变化仍可能与生物等效性声明兼容。例如，当参比制剂和受试制剂的个体内变异系数分别为40%和38%时，均值之间的允许差异可能会作为一种益处增加12.3%。如果参比产品和受试产品的个体内变异分别为40%和42%，则会导致11.2%的惩罚。此外，还模拟了4周期交叉试验。两种制剂估计方差的比率遵循F分布。根据权衡关系计算均值之间允许偏差的变化分布；通常会以高概率注意到显著变化。例如，个体内变异为30%时，估计有37%的概率在均值之间的允许差异中偶然获得10%或更大的益处增加，还有36%的概率遭受允许差异减少10%或更大的惩罚。个体内变异为40%时，均值之间允许差异分别扩大和缩小10%的估计概率分别为42%和另外42%。因此，这种权衡的强烈不对称可能导致益处和惩罚的概率非常大。所以，所研究的评估个体生物等效性的模型似乎不适合实施。
